Reflection map baking
Not really my area of expertise, but depending on what you want you could try baking a texture from a glossy sphere.


Create a new UV Sphere, you may want to make it an all quads mesh
first by removing the top and bottom vertex, then selecting the
first open edge loop, and extruding it, then scale it to zero so
that all vertex merge at the center, but don't remove doubles.
Mark a seam along one of its vertical loops and select one random
face. Now Unwrap it using the Active Quads option. In the image
editor it should wield a perfect orthogonal grid mesh.
You can now assign a perfectly glossy material to the sphere and use
it to bake an environment map of your island.


I have not tried it myself, but it should work; I used a similar technique under Cycles render to create a cube map environment